"Roy is going to do a little tuneup fight, get back in the ring and see how he feels," Wright said. "He's been training for the fight for about six weeks already."

Jones, once the untouchable king of boxing and winner of titles in four weight classes from middleweight to heavyweight, will try to rebound from a nasty 10th-round knockout loss May 21 to Denis Lebedev in Moscow.

Although Jones was headed for a split-decision loss to Lebedev, he was far more competitive than most thought he would be -- until Lebedev, a top cruiserweight contender, rendered him unconscious with two seconds left in the bout.

"I think Roy just doesn't want to go out on a loss," Wright said. "He wants to see how he feels and see if he wants to go any further. With Lebedev, he was in the fight until the last 10 seconds and Lebedev is the No. 1 contender. It ain't like Roy can't compete."

Jones (54-8, 40 KOs) also lost his previous two bouts, a lopsided decision to Bernard Hopkins and a first-round knockout to Danny Green in Australia.

Jones' career has been in a downward spiral since he won a majority decision against Antonio Tarver in their first light heavyweight championship fight in 2003. Since then, Jones is 5-7, and four of the losses came by knockout.

Wright said that because many are worried about Jones' health as he continues to box, he recently went through an exhaustive physical. Jones was already in training when he visited the Mayo Clinic in Rochester, Minn., about six weeks ago, Wright said.

"We sent him to the Mayo Clinic and he got a clean bill of health," Wright said. "Had a full physical, everything they do, and they said he was fit to fight, perfect condition. We wanted to see if he was able to fight, or if he had anything wrong with him, and they said no."

Jones would appear to be facing a safe opponent in the 30-year-old Alexander (14-5-2, 2 KOs).

Alexander, of Camden. N.J., is 0-5-1 in his past six fights, going the distance each time, and has not fought since October 2009. He is best known for participating in the 2007 edition of the reality series "The Contender."

He was eliminated from the tournament in the first round and has not won since.

Wright's view of the match for Jones is simple.

"If you can't beat him, you need to stop," he said.

Dan Rafael is the senior boxing writer for ESPN.com. Follow him on Twitter @danrafaelespn.